Abstract : Recent developments in the area of stereoscopic displays and tracking technologies have paved the way to combine touch interaction on interactive surfaces with spatial interaction above the surface of a stereoscopic display. This holistic design space supports novel affordances and user experiences during touch interaction, but also induce challenges to the interaction design. In this paper we introduce the concept of hover interaction for such setups. Therefore, we analyze the non-visual volume above a virtual object, which is perceived as the corresponding hover space for that object. The results show that the users’ perceptions of hover spaces can be categorized into two groups. Either users assume that the shape of the hover space is extruded and scaled towards their head, or along the normal vector of the interactive surface. We provide a corresponding model to determine the shapes of these hover spaces, and confirm the findings in a practical application. Finally, we discuss important implications for the development of future touch-sensitive interfaces.